The next day, Elizabeth takes a walk. She finds Darcy waiting for her. He gives her a letter of explanation. In the letter, Darcy answers Elizabeth's charges of misconduct toward Jane and Wickham. He knew that Bingley was in love with Jane, but he detected no affection on her part and, given that, thought it unwise for Bingley to become attached to Elizabeth's family, with its improprieties and lack of wealth. In London, he joined with Caroline in convincing Bingley to give up the attachment. Darcy also confesses, with regret, to keeping Bingley from finding out that Jane was in London, too.
In Chapter 6, Charlotte warned Elizabeth that Jane needed to show her affections for Bingley. It turns out she was right, and that Darcy interpreted Jane's reserve as a lack of love for Bingley. In conjunction with the Bennets' tastelessness at the ball, he believed that the marriage was not in Bingley's interest. However, he does not admit he crossed the line by lying to Bingley.
Regarding Wickham, Darcy says that after Darcy's father died, Wickham resigned his opportunity with the church in exchange for money for law school. Rather than using the money to attend law school, though, he spent it on partying. When the money ran out, he asked Darcy for more money, and was furious when Darcy refused.
Wickham turns out to be a classic example of a corrupt, directionless opportunist. In this case, Darcy's pride meant that he refused to meet Wickham's demands. In other words, he wouldn't let Wickham use him.
Years passed. Wickham saw an opportunity with Darcy's sister Georgiana, who was both rich and, at age 15, naÏve. Wickham charmed her into eloping with him, but Darcy discovered their plans and sent Wickham away. To protect his sister's reputation, Darcy has kept everything a secret. He refers Elizabeth to Colonel Fitzwilliam to confirm the story.
Wickham tried to seduce and marry Georgiana merely for her money. Darcy keeps it secret because even Georgiana's willingness to run off with Wickham could ruin her reputation and wreck her own chance at a good marriage.